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.. [1] http://docs.python.org/library/itertools.html#recipes

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        >>> i = (x for x in range(10))
        >>> next(i)
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        >>> next(i)
        4
        >>> consume(i)
        >>> next(i)
        Traceback (most recent call last):
          File "<stdin>", line 1, in <module>
        StopIteration

    If the iterator has fewer items remaining than the provided limit, the
    whole iterator will be consumed.

        >>> i = (x for x in range(3))
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	r4cGs&|durt|t|��St|t||��S)aKCall *function* with *args* repeatedly, returning an iterable over the
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        >>> args = 3, 5
        >>> list(repeatfunc(add, times, *args))
        [8, 8, 8, 8]

    If *times* is ``None`` the iterable will not terminate:

        >>> from random import randrange
        >>> times = None
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    iterables whose length is not a multiple of *n*.

    When *incomplete* is `'fill'`, the last group will contain instances of
    *fillvalue*.

    >>> list(grouper('ABCDEFG', 3, incomplete='fill', fillvalue='x'))
    [('A', 'B', 'C'), ('D', 'E', 'F'), ('G', 'x', 'x')]

    When *incomplete* is `'ignore'`, the last group will not be emitted.

    >>> list(grouper('ABCDEFG', 3, incomplete='ignore', fillvalue='x'))
    [('A', 'B', 'C'), ('D', 'E', 'F')]

    When *incomplete* is `'strict'`, a `ValueError` will be raised.

    >>> iterator = grouper('ABCDEFG', 3, incomplete='strict')
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        >>> is_odd = lambda x: x % 2 != 0
        >>> iterable = range(10)
        >>> even_items, odd_items = partition(is_odd, iterable)
        >>> list(even_items), list(odd_items)
        ([0, 2, 4, 6, 8], [1, 3, 5, 7, 9])

    If *pred* is None, :func:`bool` is used.

        >>> iterable = [0, 1, False, True, '', ' ']
        >>> false_items, true_items = partition(None, iterable)
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        ([0, False, ''], [1, True, ' '])

    Nc3s>�	|r|��V|s�D]}�|�r�n��|�ndSq�N)�popleft�append)�queue�value�Zfalse_queuerur{Z
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        >>> list(powerset([1, 2, 3]))
        [(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)]

    :func:`powerset` will operate on iterables that aren't :class:`set`
    instances, so repeated elements in the input will produce repeated elements
    in the output.

        >>> seq = [1, 1, 0]
        >>> list(powerset(seq))
        [(), (1,), (1,), (0,), (1, 1), (1, 0), (1, 0), (1, 1, 0)]

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        >>> list(unique_everseen('AAAABBBCCDAABBB'))
        ['A', 'B', 'C', 'D']
        >>> list(unique_everseen('ABBCcAD', str.casefold))
        ['A', 'B', 'C', 'D']

    Raises ``TypeError`` for unhashable items.

    Some unhashable objects can be converted to hashable objects
    using the *key* parameter:

    * For ``list`` objects, try ``key=tuple``.
    * For ``set`` objects, try ``key=frozenset``.
    * For ``dict`` objects, try ``key=lambda x: frozenset(x.items())``
      or in Python 3.15 and later, set ``key=frozendict``.

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    >>> list(unique_justseen('ABBCcAD', str.lower))
    ['A', 'B', 'C', 'A', 'D']

    Nrr�)rjr$rrt)rgrwrhrhrira�s	racCst|||d�}t||d�S)a�Yields unique elements in sorted order.

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    >>> list(unique('ABBcCAD', str.casefold))
    ['A', 'B', 'c', 'D']
    >>> list(unique('ABBcCAD', str.casefold, reverse=True))
    ['D', 'c', 'B', 'A']

    The elements in *iterable* need not be hashable, but they must be
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    )rw�reverse)rw)�sortedra)rgrwr�Z	sequencedrhrhrir_	sr_ccs<�t|��|dur|�V	|�Vq1swYdS)a�Yields results from a function repeatedly until an exception is raised.

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        >>> l = [0, 1, 2]
        >>> list(iter_except(l.pop, IndexError))
        [2, 1, 0]

    Multiple exceptions can be specified as a stopping condition:

        >>> l = [1, 2, 3, '...', 4, 5, 6]
        >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError)))
        [7, 6, 5]
        >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError)))
        [4, 3, 2]
        >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError)))
        []

    Nr)rk�	exceptionrxrhrhrir7s�
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        >>> first_true(range(10))
        1
        >>> first_true(range(10), pred=lambda x: x > 5)
        6
        >>> first_true(range(10), default='missing', pred=lambda x: x > 9)
        'missing'

    )rt�filter)rgrvr{rhrhrir2:sr2r��rcGs ttt|��|}ttt|��S)a�Draw an item at random from each of the input iterables.

        >>> random_product('abc', range(4), 'XYZ')  # doctest:+SKIP
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    drawn from each iterable.

        >>> random_product('abcd', range(4), repeat=2)  # doctest:+SKIP
        ('a', 2, 'd', 3)

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    )r~rjr()rr�ZpoolsrhrhrirMNsrMcCs*t|�}|durt|�n|}tt||��S)abReturn a random *r* length permutation of the elements in *iterable*.

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        >>> random_permutation(range(5))  # doctest:+SKIP
        (3, 4, 0, 1, 2)

    This equivalent to taking a random selection from
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        (0, 0, 1, 2, 2)

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    c3s�|]}t��VqdSr�)r&r��rfrhrir��s�z6random_combination_with_replacement.<locals>.<genexpr>cr�rhrhr�r�rhrir��r�z7random_combination_with_replacement.<locals>.<listcomp>)r~ror�r�)rgr�r�rh)rfr�rirI�srIcCs�t|�}t|�}t||�}|dkr||7}d|kr |ks#t�t�g}|r[||||d|d}}}||krP||8}|||||d}}||ks;|�|d|�|s't|�S)a�Equivalent to ``list(combinations(iterable, r))[index]``.

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    sort position *index* directly, without computing the previous
    subsequences.

        >>> nth_combination(range(5), 3, 5)
        (0, 3, 4)

    ``ValueError`` will be raised If *r* is negative.
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        ['0', '1', '2', '3']

    To prepend multiple values, see :func:`itertools.chain`
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    )r
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    For example, multiplying ``(x² -x - 20)`` by ``(x - 3)``
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        >>> list(convolve([1, -1, -20], [1, -3]))
        [1, -4, -17, 60]

    Examples of popular kinds of kernels:

    * The kernel ``[0.25, 0.25, 0.25, 0.25]`` computes a moving average.
      For image data, this blurs the image and reduces noise.
    * The kernel ``[1/2, 0, -1/2]`` estimates the first derivative of
      a function evaluated at evenly spaced inputs.
    * The kernel ``[1, -2, 1]`` estimates the second derivative of a
      function evaluated at evenly spaced inputs.

    Convolutions are mathematically commutative; however, the inputs are
    evaluated differently.  The signal is consumed lazily and can be
    infinite. The kernel is fully consumed before the calculations begin.

    Supports all numeric types: int, float, complex, Decimal, Fraction.

    References:

    * Article:  https://betterexplained.com/articles/intuitive-convolution/
    * Video by 3Blue1Brown:  https://www.youtube.com/watch?v=KuXjwB4LzSA

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         >>> ''.join(all_upper)
         'ABC'
         >>> ''.join(remainder) # takewhile() would lose the 'd'
         'dEfGhI'

    Note that the first iterator must be fully consumed before the second
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    )rrrr�)�	predicate�itZtruesZafterrhrhrir.�sr.cCs:t|d�\}}}t|d�t|d�t|d�t|||�S)z�Return overlapping triplets from *iterable*.

    >>> list(triplewise('ABCDE'))
    [('A', 'B', 'C'), ('B', 'C', 'D'), ('C', 'D', 'E')]

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        >>> list(sliding_window(range(6), 4))
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    If *iterable* has fewer than *n* items, then nothing is yielded:

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        []

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    ��r�zn should be at least one, not )r�r�rr�r�rrhrhrirV%s

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    r�r�)	rer�slicerr�rorjr!r)rg�seqZslicesrhrhrirW>s	rWcCs(dg}|D]}tt|d|f��}q|S)ukCompute a polynomial's coefficients from its roots.

    >>> roots = [5, -4, 3]            # (x - 5) * (x + 4) * (x - 3)
    >>> polynomial_from_roots(roots)  # x³ - 4 x² - 17 x + 60
    [1, -4, -17, 60]

    Note that polynomial coefficients are specified in descending power order.

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    >>> list(iter_index('AABCADEAF', 'A', 1))  # start index is inclusive
    [1, 4, 7]
    >>> list(iter_index('AABCADEAF', 'A', 1, 7))  # stop index is not inclusive
    [1, 4]

    The behavior for non-scalar *values* matches the built-in Python types.

    >>> list(iter_index('ABCDABCD', 'AB'))
    [0, 4]
    >>> list(iter_index([0, 1, 2, 3, 0, 1, 2, 3], [0, 1]))
    []
    >>> list(iter_index([[0, 1], [2, 3], [0, 1], [2, 3]], [0, 1]))
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        >>> list(reshape(matrix, cols))
        [(0, 1, 2), (3, 4, 5)]

    If *shape* is a tuple (or other iterable), the input matrix can have
    any number of dimensions. It will first be flattened and then rebuilt
    to the desired shape which can also be multidimensional:

        >>> matrix = [(0, 1), (2, 3), (4, 5)]    # Start with a 3 x 2 matrix

        >>> list(reshape(matrix, (2, 3)))        # Make a 2 x 3 matrix
        [(0, 1, 2), (3, 4, 5)]

        >>> list(reshape(matrix, (6,)))          # Make a vector of length six
        [0, 1, 2, 3, 4, 5]

        >>> list(reshape(matrix, (2, 1, 3, 1)))  # Make 2 x 1 x 3 x 1 tensor
        [(((0,), (1,), (2,)),), (((3,), (4,), (5,)),)]

    Each dimension is assumed to be uniform, either all arrays or all scalars.
    Flattening stops when the first value in a dimension is a scalar.
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    [(49, 80), (41, 60)]

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    r)ror-rr�rr])Zm1Zm2rfrhrhrir:sr:cCs�td|�D]7}d}}d}|dkr4||||}||||}||||}t|||�}|dks||kr<|Sqtd��)Nr�r�zprime or under 5)r�rr�)rf�br��y�drhrhri�_factor_pollards��r���ccs��|dkrdStD]}||s|V||}||rq	g}|dkr$|gng}|D]}|dks2t|�r8|�|�q(t|�}||||f7}q(t|�EdHdS)aYield the prime factors of n.

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    [2, 2, 2, 3, 3, 5]

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    >>> x = 2.5
    >>> polynomial_eval(coefficients, x)
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    )r�rr|rhrhrirXesrXcCs&t|�}ttd|��}ttt||��S)u�Compute the first derivative of a polynomial.

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    >>> derivative_coefficients
    [3, -8, -17]

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    r�)ror�r�rerjr )r�rfr�rhrhrirDpsrDcCs"tt|��D]}|||8}q|S)u�Return the count of natural numbers up to *n* that are coprime with *n*.

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    >>> n = 9
    >>> totient(n)
    6

    >>> totatives = [x for x in range(1, n) if gcd(n, x) == 1]
    >>> totatives
    [1, 2, 4, 5, 7, 8]
    >>> len(totatives)
    6

    Reference:  https://en.wikipedia.org/wiki/Euler%27s_totient_function

    )r�r3)rfr�rhrhrir\�sr\))i�)r�)i��)��I)l�tT7)r���=)l�ay)r��
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        True
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        >>> is_prime(18_446_744_073_709_551_557)
        True

    Find the next prime over one billion:

        >>> next(filter(is_prime, count(10**9)))
        1000000007

    Generate random primes up to 200 bits and up to 60 decimal digits:

        >>> from random import seed, randrange, getrandbits
        >>> seed(18675309)

        >>> next(filter(is_prime, map(getrandbits, repeat(200))))
        893303929355758292373272075469392561129886005037663238028407

        >>> next(filter(is_prime, map(randrange, repeat(10**60))))
        269638077304026462407872868003560484232362454342414618963649

    This function is exact for values of *n* below 10**24.  For larger inputs,
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    * There are 1260 distinct ways to arrange 9 balls consisting of 3 reds, 4
      greens, and 2 blues.

    * There are 1260 unique ways to place 9 distinct objects into three bins
      with sizes 3, 4, and 2.

    The :func:`multinomial` function computes the length of
    :func:`distinct_permutations`.  For example, there are 83,160 distinct
    anagrams of the word "abracadabra":

        >>> from more_itertools import distinct_permutations, ilen
        >>> ilen(distinct_permutations('abracadabra'))
        83160

    This can be computed directly from the letter counts, 5a 2b 2r 1c 1d:

        >>> from collections import Counter
        >>> list(Counter('abracadabra').values())
        [5, 2, 2, 1, 1]
        >>> multinomial(5, 2, 2, 1, 1)
        83160

    A binomial coefficient is a special case of multinomial where there are
    only two categories.  For example, the number of ways to arrange 12 balls
    with 5 reds and 7 blues is ``multinomial(5, 7)`` or ``math.comb(12, 5)``.

    Likewise, factorial is a special case of multinomial where
    the multiplicities are all just 1 so that
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    For example:

        >>> list(running_median([5.0, 9.0, 4.0, 12.0, 8.0, 9.0]))
        [5.0, 7.0, 5.0, 7.0, 8.0, 8.5]
        >>> list(running_median([5.0, 9.0, 4.0, 12.0, 8.0, 9.0], maxlen=3))
        [5.0, 7.0, 5.0, 9.0, 8.0, 9.0]

    Supports numeric types such as int, float, Decimal, and Fraction,
    but not complex numbers which are unorderable.

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        >>> list(running_mean([40, 30, 50, 46, 39, 44]))
        [40.0, 35.0, 40.0, 41.5, 41.0, 41.5]

        >>> list(running_mean([40, 30, 50, 46, 39, 44], maxlen=3))
        [40.0, 35.0, 40.0, 42.0, 45.0, 43.0]

    Supports numeric types such as int, float, complex, Decimal, and Fraction.

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    Nr�rr)rqrjr%rrr�r
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    For example:

        >>> list(running_min([4, 3, 7, 0, 8, 1, 6, 2, 9, 5]))
        [4, 3, 3, 0, 0, 0, 0, 0, 0, 0]

        >>> list(running_min([4, 3, 7, 0, 8, 1, 6, 2, 9, 5], maxlen=3))
        [4, 3, 3, 0, 0, 0, 1, 1, 2, 2]

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    N��funcrr)rqr�minr�rr	rhrhrirS��
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    Set *maxlen* to a positive integer to specify the maximum size
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    For example:

        >>> list(running_max([4, 3, 7, 0, 8, 1, 6, 2, 9, 5]))
        [4, 4, 7, 7, 8, 8, 8, 8, 9, 9]

        >>> list(running_max([4, 3, 7, 0, 8, 1, 6, 2, 9, 5], maxlen=3))
        [4, 4, 7, 7, 8, 8, 8, 6, 9, 9]

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    Nrrr)rqrrrr�rr	rhrhrirP�rrP)�frozen�slotsc@s6eZdZUeed<eed<eed<eed<eed<dS)r+rsZminimumZmedianZmaximum�meanN)�__name__�
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    Yields instances of a ``Stats`` dataclass with fields for the dataset *size*,
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    �Nr�rm)rrjr+rr
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